Despite the rigorous global efforts to control SARS-CoV-2 transmission, it continues to pose a serious threat to humans with the frequent emergence of new variants. Thus, robust therapeutics to combat the virus are a desperate need. The SARS-CoV-2 spike (S) protein is an important target protein as it mediates the entry of the virus inside the host cells, which is initiated by the binding of the receptor-binding domain (RBD) to its cognate receptor, angiotensin-converting enzyme 2 (ACE-2). Herein, the inhibition potential of several naturally occurring coumarins was investigated against the spike proteins of SARS-CoV-2 variants using computational approaches. Molecular docking studies revealed 26 coumarins with better binding energies than the reference ligands, molnupiravir and ceftazidime, against the S-RBD of the omicron variant. The top 10 best-docked coumarins were further analyzed to understand their binding interactions against the spike proteins of other variants (wild-type, Alpha, Beta, Gamma, and Delta), and these studies also demonstrated decent binding energies. Physicochemical, QSAR, and pharmacokinetics analyses of the coumarins revealed wedelolactone as the best inhibitor of the spike protein with ideal Lipinski's drug-likeness and optimal ADMET properties. Furthermore, coarse-grained molecular dynamics (MD) simulation studies of spike protein-wedelolactone complexes validated the stable binding of wedelolactone in the respective binding pockets. As an outcome, wedelolactone could be utilized to develop a potent drug candidate against COVID-19 by blocking the viral entry into the host cell.